Stem cell technology is so crude at this stage that it will be at least 100 years before we can reliably grow an entire limb. We could probably regrow a limb by cloning an individual for harvesting parts from (like in The Island), but that would be unethical.
Even if we could regrow a limb, the problem would be interfacing that limb with your existing brain and spine. Blood vessels, bones, and muscles from a transplanted limb could be put together, though it would be a 5-10+ hour procedure requiring multiple surgeons.
But nerves cannot so easily be reconnected. This is why people with spinal cord injuries remain parapalegic after. The nerves do not regrow or reconnect, and we have no reliable way of making them cooperate.
So short answer is no. The advances required in medical science to pull this off would be incredible.
The better solution is likely to make human growth hormone more widely available to short kids so they don't have to do any of this at all. Though that approach creates other problems as well.